Maple 2019 Questions and Posts

These are Posts and Questions associated with the product, Maple 2019

Maple pdsolve supports periodic boundary conditions. So I was hoping it will be able to solve the heat PDE inside disk with periodic boundary conditions. But I am not able to make it work. 

Is there a trick to make Maple solve this, is there something I need to add or adjust something else? or it is just the functionality is not currently implemented?

This is what I tried

restart;

pde := diff(u(r,theta,t),t)=diff(u(r,theta,t),r$2) + 1/r*diff(u(r,theta,t),r)+1/r^2*diff(u(r,theta,t),theta$2);
bc1 := u(a,theta,t)=0;
bc2 := eval(diff(u(r,theta,t),theta),theta=-Pi)=eval(diff(u(r,theta,t),theta),theta=Pi);
bc3 := u(r,-Pi,t)=u(r,Pi,t);
ic  := u(r,theta,0)=f(r,theta);
sol := pdsolve([pde, bc1,bc2,bc3, ic], u(r, theta, t), HINT = boundedseries(r = 0)) assuming a>0,r>0

I solved this analytically by hand using standard separation of variables method. The issue of telling Maple the solution is bounded at center of disk, I assume is being handled automatically by the HINT=boundedseries(r = 0).

If I remove the hint, it also does not solve it. 

Maple 2019, Physics package 338

For this problem

I'd like to see if Maple can give, or simplify the solution it now gives to look like this solution 

The one it currently gives is

restart;

pde:=diff(w(x,t),t)+c*diff(w(x,t),x)=0; 
ic:=w(x,0)=f(x);
bc:=w(0,t)=h(t);
sol:=pdsolve([pde,ic,bc],w(x,t))  assuming t>0,x>0,c>0

 

And I did not know how to simplify it or obtain the simpler one. I tried strip and TWS hints.  I also do not understand why Maple gives an integral with 0 as upper limit there (the second integral).

Using Physics package cloud version 338 and Maple 2019. On windows 10.

Thank you

Hello,

I´a currently making a school assigment, but i can´t get maple plots to combine the graphs i plot, when i plot multiple plots. (see picture) (the code is in the bottom of the question)


as you can see the green and yellow grafh won´t combine. I have tried google but couldn´t find any anserws that worked.
Hope someone can help me!
Thanks!
 
 
with(plots); with(Plot);
a := plot(4, x = 0 .. .25, color = red, view = [0 .. .25, 0 .. 5]);
b := plot(1/x, x = .25 .. 1.101, color = blue, view = [.25 .. 1.101, 0 .. 5]);
c := plot(-(1/12)*x+1, x = 1.01 .. 6, color = yellow, view = [1.101 .. 6, 0 .. 5]);
d := plot(.5+sqrt(x-5), x = 6 .. 20, color = green, view = [6 .. 20, 0 .. 5]);
e := plot(1.15*sqrt(x-7), x = 7 .. 20, color = pink, view = [7 .. 20, 0 .. 5]);
display(a, b, c, d, e);
 
 

Hello Maple experts;

I am not able to understand why Maple 2019 can solve Laplace PDE in 2D Catersian on semi-infinite domain, when the infinity is along the Y direction, but not along the X direction, since the solution method is exactly the same.

Here is the code

restart;

#right one, Maple can not solve
pde := diff(u(x, y), x$2)+diff(u(x, y), y$2) = 0:
bc_left_edge := u(0, y) = 0:
bc_bottom_edge:= u(x, 0) = 0:
bc_top_edge:= u(x, 1) = A:
bc:=bc_left_edge ,bc_top_edge,bc_bottom_edge:
sol:=pdsolve([pde, bc],HINT = boundedseries(x = infinity)) assuming x>0,y>0;


#left one, Maple can solve
pde := diff(u(x, y), x$2)+diff(u(x, y), y$2) = 0:
bc_left_edge := u(0, y) = 0:
bc_bottom_edge:= u(x, 0) = 0:
bc_right_edge:= u(1, y) = A:
bc:=bc_left_edge ,bc_right_edge,bc_bottom_edge:
sol:=pdsolve([pde, bc],HINT = boundedseries(y = infinity)) assuming x>0,y>0;

Here is screen shot.

Maple can solve both cases if I remove the HINT. But the solution it gives is not as simple as using the HINT and contains unknown constants (_C5) that is why I use the HINT.